is nevertheless considered a compound word since it has 3 words in it?

Yes. I would consider it a compound word as all 3 words 'inside' the word are adding meaning.

According to http://grammar.ccc.commnet.edu/grammar/compounds.htm
There are three forms of compound words:
the closed form, in which the words are melded together, such as firefly, secondhand, softball, childlike, crosstown, redhead, keyboard, makeup, notebook;